(- (- b) (sqrt (+ (pow b 2) (* 4 ac))))

Average Error: 30.4 → 30.4

Time: 1.9s

Precision: binary64

Math

\[\left(-b\right) - \sqrt{{b}^{2} + 4 \cdot ac}\]

↓

\[\left(-b\right) - \sqrt{{b}^{2} + 4 \cdot ac}\]

Error

Bits error versus b

Bits error versus ac

Derivation

1. Initial program 30.4

   \[\left(-b\right) - \sqrt{{b}^{2} + 4 \cdot ac}\]

2. Final simplification 30.4

   \[\leadsto \left(-b\right) - \sqrt{{b}^{2} + 4 \cdot ac}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (b ac)
  :name "(- (- b) (sqrt (+ (pow b 2) (* 4 ac))))"
  :precision binary64
  (- (neg b) (sqrt (+ (pow b 2.0) (* 4.0 ac)))))